The non-abelian flat directions in the tachyon potential of stable non-BPS branes recently found are shown to persist to all orders in α′ at tree level in the string theory. We also obtain the non-abelian Born-Infeld action including the tachyon potential for a stack of stable non-BPS branes on a critical orbifold. Finally we discuss stable soliton states on the non-BPS brane.